-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1113109276838883749380466993633', 'a10': [-3504382105907224400000, 0.0], 'a2': [-2097152.0, 0.0], 'a3': [-13088173376.585302, 0.0], 'a4': [4398046511104.0, 0.0], 'a5': [1671019604638683.5, 0.0], 'a6': [27447888973052620, 0.0], 'a7': [-670882601933876200, 0.0], 'a8': [-9223372036854776000, 0.0], 'a9': [-156956685058980740000, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.422079069144658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '21.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [2097152.0, 0]]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': 'CDF', 'conductor': 2, 'conductor_radical': 2, 'conjugate': '1113109276838883749380466993633', 'degree': 2, 'euler_factors': [[[1.0, 0], [2097152.0, 0]], [[1.0, 0], [13088173376.585302, 0], [328256967394537050000, 0]], [[1.0, 0], [-1671019604638683.5, 0], [1136868377216160300000000000000, 0]], [[1.0, 0], [670882601933876200, 0], [2183814375991796600000000000000000000, 0]], [[1.0, 0], [-23269951489401183000000, 0], [602400691612421950000000000000000000000000000, 0]], [[1.0, 0], [1223183041638126700000000, 0], [793531459841715600000000000000000000000000000000, 0]], [[1.0, 0], [-348170138898774100000000000, 0], [81152820641272630000000000000000000000000000000000000, 0]], [[1.0, 0], [2924591721057158700000000000, 0], [9691808871033067000000000000000000000000000000000000000, 0]], [[1.0, 0], [-225547673735443470000000000000, 0], [35834136918934220000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-4026225988055555000000000000000, 0], [764036153800772100000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-113932451055132470000000000000000, 0], [13444753212776964000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [7691999027200858000000000000000000, 0], [27081588506598106000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-31434097997350360000000000000000000, 0], [2237205297093589000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-198373523899119560000000000000000000, 0], [17343773367030268000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-1240236937157128900000000000000000000, 0], [794708560552308300000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-22837497955841300000000000000000000000, 0], [139271544806023820000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [59265198082899930000000000000000000000, 0], [14016400571769800000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-157809881080490830000000000000000000000, 0], [58773682894798150000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-1198559587455202900000000000000000000000, 0], [3320599637338792400000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-7592599495654399000000000000000000000000, 0], [40189166097495226000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [1460699543380140000000000000000000000000, 0], [132703685728275700000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [27530617227436403000000000000000000000000, 0], [3962460313228513000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-242103918264829300000000000000000000000000, 0], [33140417259670640000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [561520238578382200000000000000000000000000, 0], [666454163935483500000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-3430386336300285300000000000000000000000000, 0], [26988862047742874000000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-2995040509665252000000000000000000000000000, 0], [153397779357967760000000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-5242752290157625700000000000000000000000000, 0], [356451677033777300000000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [36888094451920285000000000000000000000000000, 0], [1834435475471559700000000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [40275047135414895000000000000000000000000000, 0], [4067610984309766000000000000000000000000000000000000000000000000000000000000000000000000, 0]], [[1.0, 0], [140596209181252120000000000000000000000000000, 0], [19159010250734755000000000000000000000000000000000000000000000000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2-1.1-c43-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 43, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [43], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2/44/a/a/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.2758799193986774, 1.2143432234107656, 1.0352427078801996, 0.7546736217038571, 0.3980492841700642, -0.001904683859456947, -0.4077422337198834, -0.7802779789569926, -1.0817303804406382, -1.2787865613098695, -1.3453528938702322, -1.264777812679875, -1.0313717777663367, -0.6511011944140485, -0.14139463817487588, 0.46993356208292225, 1.1465703865605983, 1.8462676450702027, 2.52389502895455, 3.134756535174913, 3.6379214842194227, 3.9993172611803587, 4.1943459042419855, 4.209819889582558, 4.045061679448515, 3.712073334891745, 3.234752266108554, 2.647201831535592, 1.9912555154627887, 1.3133954161327084, 0.6612948646391799, 0.08024715433968371, -0.3902452146519284, -0.7194550323475406, -0.8877523760495929, -0.8880763463569379, -0.726432852676082, -0.4213697375658447, -0.002460754365885717, 0.49209083678469867, 1.0185463238908021, 1.531181743827645, 1.986012161123649, 2.3443893149198747, 2.5761772590545937, 2.6622401164776353, 2.596027960377755, 2.3841174781638466, 2.0456481823271577, 1.6106859423332602, 1.1176361804879555, 0.609911653154721, 0.13212718951184396, -0.27386003292659933, -0.5727256780442749, -0.73893780744987, -0.7592061439770275, -0.6338891645520428, -0.3772117405393526, -0.01624588685864332, 0.4112858547236165, 0.8602198372772535, 1.2819150949311633, 1.6286389381516873, 1.857994662335825, 1.9369966259567064, 1.8454174800956722, 1.5780859397768703, 1.1458976287257456, 0.5754097746339301, -0.09298597528614083, -0.8081902034673578, -1.5125780726850724, -2.1468903632786303, -2.6554111342493734, -2.9909710342711824, -3.119317437782064, -3.022437112140095, -2.700501464140936, -2.1722221683767486, -1.4735463430589721, -0.6547729751231978, 0.22367800302133128, 1.0964800345718022, 1.8991315766617487, 2.5736781510919102, 3.073885729538622, 3.3693657781606112, 3.448241279083485, 3.3180746995949186, 3.0049417781013923, 2.550714161336538, 2.008792149377781, 1.4386882614741006, 0.8999863590236251, 0.44627587976530875, 0.1196770067251704, -0.05347343568466446, -0.0653114147557526, 0.07279657780930424, 0.3315409496231722, 0.6669036330899261, 1.0250341841673123, 1.3482794803169649, 1.5817428341805175, 1.6796740619492614, 1.6109900661614995, 1.3632987698622245, 0.9449427591334039, 0.3847799342037907, -0.27034276732144014, -0.9602144975140121, -1.617538213093382, -2.1752170914678373, -2.5738721096912327, -2.7687609107479614, -2.735306107539411, -2.4725689179280343, -2.0042107554995883, -1.3767510417645157, -0.6552264583410797, 0.08334721472564445, 0.7580482375273477, 1.292799033586158, 1.6248303821186705, 1.711898004818704, 1.5374012181007088, 1.1127661243661047, 0.4767492747775224, -0.3083392216633668, -1.1631396994533165, -1.9997957673286724, -2.731621701692494, -3.2827956399467, -3.5969586686312254, -3.6437001073933706, -3.4221334010302096, -2.9610923967358316, -2.3158686371515143, -1.5618215618703164, -0.7855759088205857, -0.07482656001654257, 0.4920393620851684, 0.8552472053537271, 0.9807178706541086, 0.8640334054811286, 0.5307598211998199, 0.03304751443807643, -0.5571035173600521, -1.157097108035629, -1.6843604270899646, -2.0669802603532403, -2.252978994694823, -2.217003246822453, -1.9635119191902153, -1.5259922738659464, -0.9622484263860702, -0.34633078942209705, 0.2418617615251607, 0.7279365414980584, 1.0537833606441167, 1.1862745534388937, 1.1226318783868265, 0.8916227941302399, 0.5502956190239643, 0.17656780784747703, -0.1414364295882118, -0.31792413716201107, -0.2821660063403708, 0.010343336086617447, 0.5699081419346964, 1.369064932369919, 2.344087195436498, 3.4015441149761827, 4.429196991094464, 5.309893449192784, 5.936661103099862, 6.226978850392133, 6.134254790097359, 5.654866991494131, 4.82969014594201, 3.7397653841531606, 2.4965738043897883, 1.228134871375127, 0.06275945863022875, -0.8873472898683786, -1.5403751294043297, -1.8550887104455904, -1.8354457750887807, -1.52896959961387, -1.0190746532666077, -0.4124158601765507, 0.17693604911803068, 0.6442088261141382, 0.909094014416662, 0.9271283547889263, 0.6955960517779212, 0.25305926674693857, -0.3274250827247034, -0.9503857411715451, -1.5134777405997666, -1.924092120862319, -2.1144472913630095, -2.0527748017890644, -1.7487876448837214, -1.2524894004990812, -0.6464189499824089, -0.032469767132461136, 0.484689364752313, 0.8149784878021359, 0.8982571229193286, 0.7151212932736838, 0.29127903598088045, -0.30537287504085386, -0.9746890737775583, -1.5998044850759396, -2.06587591260911, -2.2790699880582177, -2.1827050289567427, -1.7678272625639455, -1.0763286701548826, -0.19587387303858028, 0.7527818419876448, 1.6342420536239235, 2.3198490147953184, 2.7085950615034626, 2.7441455937056536, 2.425092252951067, 1.8065818131965536, 0.992826742399985, 0.12148266887625787, -0.6577649230683461, -1.207055567393249, -1.4228209392231896, -1.2531754143442821, -0.7072952590860373, 0.144890917623099, 1.1828145326469004, 2.253681519789997, 3.1962916934798162, 3.8664271536740724, 4.1596613882002025, 4.027820033354638, 3.4863447032823682, 2.6113113550287625, 1.5265867936023787, 0.3832781540495421, -0.6650482895728527, -1.4871651292601218, -1.9947687460845707, -2.155340832565134, -1.995116652641067, -1.5917249662495487, -1.057892683002011, -0.5192050608702904, -0.08999036135555791, 0.1482458166853022], 'positive_zeros': ['0.878088391737027664620773659111536', '2.50392942226333406092493706108981', '5.47618812107195880219590385619644', '6.68061998450529215251991083419488', '9.193784287915135026032990493736537', '10.37818656545802728097423779032444', '12.28126007326664453601815168481033', '14.36971796286312416058226775267608', '16.97653324333278657278071332347951', '17.33080688422186730237448576095269'], 'prelabel': '2-2-1.1-c43-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.839636253805099, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c43-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.878088391737027664620773659112', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.50392942226333406092493706109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47618812107195880219590385620', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 23.422079069144658, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2/44/a/a/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-2-1.1-c43-0-1', 'motivic_weight': 43, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [43], 'order_of_vanishing': 0, 'prelabel': '2-2-1.1-c43-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.839636253805099, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c43-0', 'z1': {'__RealLiteral__': 0, 'data': '0.878088391737027664620773659112', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1113109276838883749380466993633', 'Lhash_array': ['1113109276838883749380466993633'], 'label': '2-2-1.1-c43-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/44/a/a/1/1'}